In this article it is shown that any family of curves can be altered into a semi-stable family. This implies that if is an excellent scheme of dimension at most 2 and is a separated integral scheme of finite type over , then can be altered into a regular scheme. This result is stronger then the results of [ Smoothness, semi-stability and alterations to appear in Publ. Math. IHES]. In addition we deal with situations where a finite group acts.
Dans l’article on prouve que toute famille de courbes peut être altérée en une famille semi-stable. Soit un schéma excellent de dimension 0, 1 ou 2 et soit un schéma séparé de type fini sur . Alors le résultat implique qu’on peut altérer en un schéma régulier. C’est un résultat plus fort que ceux de [Smoothness, semi-stability and alterations à paraître dans Publ. Math. IHES]. De plus, on considère des situations où un groupe fini agit, et on obtient des résultats analogues.
@article{AIF_1997__47_2_599_0, author = {Jong, A. Johan de}, title = {Families of curves and alterations}, journal = {Annales de l'Institut Fourier}, pages = {599--621}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {47}, number = {2}, year = {1997}, doi = {10.5802/aif.1575}, mrnumber = {98f:14019}, zbl = {0868.14012}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1575/} }
TY - JOUR AU - Jong, A. Johan de TI - Families of curves and alterations JO - Annales de l'Institut Fourier PY - 1997 SP - 599 EP - 621 VL - 47 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1575/ DO - 10.5802/aif.1575 LA - en ID - AIF_1997__47_2_599_0 ER -
Jong, A. Johan de. Families of curves and alterations. Annales de l'Institut Fourier, Volume 47 (1997) no. 2, pp. 599-621. doi : 10.5802/aif.1575. http://www.numdam.org/articles/10.5802/aif.1575/
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